ANALYSIS OF PLANT GROWTH DYNAMICS UNDER THE EFFECT OF TOXICITY: A DELAY DIFFERENTIAL EQUATION MODEL
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Abstract
A mathematical model is designed to examine plant growth under stress in the presence of toxicity with a delay. It is observed that toxic substances change the soil's structure and activity, which has a negative impact on the concentration of nutrients there. The availability of soil nutrients is one of the most significant elements affecting biomass. Total biomass is seen to be adversely affected by both nutrition deficiency and toxicity. It has been noted that the presence of toxicity changes the physiology and growth of the plant, which ultimately reduces crop growth and production. This adverse effect of toxicity is not seen immediately, but after an incubation period. This effect is demonstrated by taking into account the delay in the state variable. Additionally, Hopf bifurcation is observed for the crucial value of the delay parameter. Utilizing explicit techniques, the direction and stability of bifurcating periodic solutions are found. Sensitivity analysis is used to determine the sensitivity of solutions of the model when values of parameters are varied. MATLAB is used for simulation.
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